数列题 1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100=多少?

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数列题 1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100=多少?

数列题 1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100=多少?
数列题 1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100=多少?

数列题 1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100=多少?
原式=1/2+1/6+1/12+...+1/9900
=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(99×100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
=1-1/100
=99/100
解答的很详细了,应该可以看的很清楚.祝学习愉快!

1*1/2+1/2*1/3+1/3*1/4+1/4*1/5+...+1/99*1/100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/99-1/100
=1-1/100
=99/100

1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+...+1/99×1/100
=1-1/1/2-1/3+1/3-1/4+.....+1/99-1/100
=1-1/100
=99/100

99/100
原式等于 1-1/2+1/2-1/3---1/99-1/100 等于1-1/100

1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100=1-1/100=99/100

等于99/100 上式等于1-1/2+1/2-1/3~~~~~~~-1/100=